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Runti Compl Inner Rewri 22807 pair #381904413
details
property
value
status
complete
benchmark
sizeChange.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n070.star.cs.uiowa.edu
space
AProVE_06
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.435323 seconds
cpu usage
320.607888502
max memory
5.496131584E9
stage attributes
key
value
output-size
19839
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^2)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). (0) CpxTRS (1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (2) CdtProblem (3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CdtProblem (5) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CdtProblem (7) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CdtProblem (9) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CdtProblem (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 20 ms] (12) CdtProblem (13) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CdtProblem (15) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 45 ms] (16) CdtProblem (17) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 40 ms] (18) CdtProblem (19) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (20) BOUNDS(1, 1) (21) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (22) TRS for Loop Detection (23) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (24) BEST (25) proven lower bound (26) LowerBoundPropagationProof [FINISHED, 0 ms] (27) BOUNDS(n^1, INF) (28) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: r(xs, ys, zs, nil) -> xs r(xs, nil, zs, cons(w, ws)) -> r(xs, xs, cons(succ(zero), zs), ws) r(xs, cons(y, ys), nil, cons(w, ws)) -> r(xs, xs, cons(succ(zero), nil), ws) r(xs, cons(y, ys), cons(z, zs), cons(w, ws)) -> r(ys, cons(y, ys), zs, cons(succ(zero), cons(w, ws))) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (2) Obligation: Complexity Dependency Tuples Problem Rules: r(z0, z1, z2, nil) -> z0 r(z0, nil, z1, cons(z2, z3)) -> r(z0, z0, cons(succ(zero), z1), z3) r(z0, cons(z1, z2), nil, cons(z3, z4)) -> r(z0, z0, cons(succ(zero), nil), z4) r(z0, cons(z1, z2), cons(z3, z4), cons(z5, z6)) -> r(z2, cons(z1, z2), z4, cons(succ(zero), cons(z5, z6))) Tuples: R(z0, z1, z2, nil) -> c R(z0, nil, z1, cons(z2, z3)) -> c1(R(z0, z0, cons(succ(zero), z1), z3)) R(z0, cons(z1, z2), nil, cons(z3, z4)) -> c2(R(z0, z0, cons(succ(zero), nil), z4)) R(z0, cons(z1, z2), cons(z3, z4), cons(z5, z6)) -> c3(R(z2, cons(z1, z2), z4, cons(succ(zero), cons(z5, z6)))) S tuples: R(z0, z1, z2, nil) -> c R(z0, nil, z1, cons(z2, z3)) -> c1(R(z0, z0, cons(succ(zero), z1), z3)) R(z0, cons(z1, z2), nil, cons(z3, z4)) -> c2(R(z0, z0, cons(succ(zero), nil), z4)) R(z0, cons(z1, z2), cons(z3, z4), cons(z5, z6)) -> c3(R(z2, cons(z1, z2), z4, cons(succ(zero), cons(z5, z6)))) K tuples:none Defined Rule Symbols: r_4 Defined Pair Symbols: R_4 Compound Symbols: c, c1_1, c2_1, c3_1 ---------------------------------------- (3) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: R(z0, z1, z2, nil) -> c ----------------------------------------
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